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I flew today from KUR to KSBA and requested flight following from the ground. Clearence delivery gave me a squak code and the departure frequency.
Shortly after takeoff, the tower asked me to contact departure as expected. After contacting departure, they responded by saying "cancel altitude restrictions".
This threw me off because I didn't know I was on altitude restrictions in the first place. KBUR clearance delivery didn't specify any restrictions (they only gave me the squak code and departure frequency), neither did the tower.

Is there some sort of understood altitude restriction when departing from a Class C airport?
Was I restricted to the altitude I specified when asking for flight following (6500), and the departure controller was simply stating I could deviate from that if I wanted to?
Or did clearance forget to to explicitly state an altitude restriction that was later cancelled by departure?

Thanks in advance. I've already learnt so much thanks to pilotedge and this community. I truly appreciate you all!

Most SoCal class C airports have pretty scripted procedures. The controller probably forgot to give the instructions to you.

Marcus Becker wrote: ... The controller probably forgot to give the instructions to you.

? really ? I'm puzzled...
Please elaborate.

From your CAT Ratings flights, you might remember the flight from SBA to BUR. The SBA clearance controller issued an altitude restriction of at or below 1500ft initially, on runway heading. ONT and SNA also have alt restrictions. BUR does, too (also from the CAT Ratings).

Thank you all for the response!

I re-did the flight, and this time the tower did specifically issue an altitude restriction, which made everything more clear to me.