> If the fraction was to stay constant deposits would increase as fast as loans.

In relative terms yes, in absolute terms, they'd be lower.

> the problem of the US banking system in the last years has been that deposits have been increasing much faster than loans

Yes, it seems to be. "Too much money chasing too few returns", as they say.

> In relative terms yes, in absolute terms, they'd be lower.

Not really. The Loan-to-Deposit ratio is usually lower than one so if both double that means that deposits grow more than loans in absolute terms.

Yeah, that's my misuse of the term "deposit" where I meant something like "total reserve amount".