Harry stepped into Gringotts, and moved to stand in the nearest line. When it was is turn he smiled politely to the goblin in charge and asked if he could be escorted to someone that could help him with claiming his inheritance.

the goblin gasped, eyes wide in shock, before quickly recomposing himself and escorting harry to another room with a plaque naming it 'Griphook, Potter Family Account Manager's office. Once harry was conveniently inside the office of the only goblin he knew, he took a seat in the surprisingly comfortable chair across the goblin in question. "Hello Griphook, I was hoping you would be able to help me claim my inheritance today." Harry smiled and said politely.
Griphook gasped like the previous goblin, "Young master wizard is remembering Griphook's name and is being polite to a goblin. Oh my god! This has never - ever happened before." The goblin said really excitedly. "Of course Mr. Potter Gringotts will of course do everything in its power to serve you."

Griphook seized Harry's hand without further ado and pricked a finger so a single drop of blood fell onto a large parchment that lay prepared on the desk. Seconds passed and quickly the scroll filled up with his family tree and all possible claims he might have for the ease of the goblins so they didn't actually have to keep records or anything so normal.
Griphook scanned the list before gasping once more, almost fainting in shock and quickly pressing a button on the desk before calming himself.

"What is it, Griphook, is something wrong." Harry asked worriedly.

"No! Never, Mr. Potter it seems you are a descendant of Merlin and the three cool founders - excluding Hufflepuff, 'cus Hufflepuff is for duffers, and Thor, and Zeus and Aphrodite, and that other really important wizard, Bob. Now that you have claimed all these accounts you are now the richest person in the world and shall never want for money." Griphook said giddily. A goblin shuffled into the room and dropped off a package before quickly leaving. "Ah! it has arrived," Griphook said happily. He unwrapped the package and pushed it across the desk toward harry, revealing in fact one ornate box and another shrunken trunk. "In the first box you shall find all the rings that signify your lordship over the various families, you need only put them on to claim them, by right of magic."

Harry eyes widened as he opened the box to reveal dozens of rings. Slowly he picked one out and put it on, watching as it glowed and resized to fit his finger. Then he picked up the next and put it on the same finger watching as the two rings quickly melded together to form a single slightly different ring. Quickly getting the gist of it Harry happily put the rest of the rings on so that they combined as well, because obviously all these past family heads would be so pleased that a single person was gaining headship and would have planned on this eventuality when making the magic of the rings. In the end he was left with a single massive ring that had elements of each and every different crest that had been on the other rings and magically it managed not to look utterly cluttered and stupid. Harry smiled at this success.

Griphook smiled too, "And of course Lord Potter, now that you have claimed your Lordship you are an Emancipated minor and can do whatever you want with your hugely massive fortune because no one thinks it's a bad idea for a child to come into such a windfall without any sort of spending limit. Also you will note that you can choose to have the ring become invisible so that its presence won't overtly affect the plot and won't inform people you don't want to know that you've gained your independence and are no longer their puppet; because of course past Lords were always terribly ashamed of their Lord status and trying to hide it." He told harry, who quickly made the ring turn invisible and completely undetectable so that he could fool the evil Dumbledore of the story who had been controlling him. "Finally Lord Potter this is a trunk we have commissioned and created just for you because you're nice to us goblins and no one else has ever done that. You will find that the trunk contains roughly a gazillion compartments all the size of a lavish suite so that you shall never need for space and each has been equipped with the best appliances so that there's no need to waste the readers time with a long boring shopping trip - this way they can just assume you have all you shall ever need conveniently at your finger tips. Good luck, Lord Potter, and know that your teeny tiny show of respect for the goblin nation was such an incredible and rare thing that we have decided to become your ally and throw the full might of our complete chokehold on the wizarding economy behind you in the coming war!"