Considering topologies of anonymous networks we used to organizing anonymous communication into hard to trace paths hiding its origin or destination. In anonymity the company is crucial, however the serial transportation imposes a costly tradeoff between a level of privacy and a speed of communication. This paper introduces a framework of a novel architecture for anonymous networks that hides initiators of communications by parallelization of anonymous links. The new approach, which is based on the grounds of the anonymous P2P network called P2Priv, does not require content forwarding via a chain of proxy nodes to assure high degree of anonymity. Contrary to P2Priv, the new architecture can be suited to anonymization of various network communications, including anonymous access to distributed as well as client-server services. In particular, it can be considered as an anonymization platform for these network applications where both privacy and low delays are required.