RDF and SPARQL provide a uniform way to publish and query billions of triples in open knowledge graphs (KGs) on the Web. Yet, provisioning of a fast, reliable, and responsive live querying solution for open KGs is still hardly possible through SPARQL endpoints alone: while such endpoints provide a remarkable performance for single queries, they typically can not cope with highly concurrent query workloads by multiple clients. To mitigate this, the Linked Data Fragments (LDF) framework sparked the design of different alternative low-cost interfaces such as Triple Pattern Fragments (TPF), that partially offload the query processing workload to the client side. On the downside, such interfaces still come with the expense of unnecessarily high network load due to the necessary transfer of intermediate results to the client, leading to query performance degradation compared with endpoints. To address this problem, in the present work, we investigate alternative interfaces, refining and extending the original TPF idea, which also aims at reducing server-resource consumption, by shipping query-relevant partitions of KGs from the server to the client. To this end, first, we align formal definitions and notations of the original LDF framework to uniformly present existing LDF implements and such “partition-based” LDF approaches. These novel LDF interfaces retrieve, instead of the exact triples matching a particular query pattern, a subset of pre-materialized, compressed, partitions of the original graph, containing all answers to a query pattern, to be further evaluated on the client side. As a concrete representative of partition-based LDF, we present smart-KG+, extending and refining our prior work (In WWW ’20: The Web Conference 2020 (2020) 984–994 ACM / IW3C2) in several respects. Our proposed approach is a step forward towards a better-balanced share of the query processing load between clients and servers by shipping graph partitions driven by the structure of RDF graphs to group entities described with the same sets of properties and classes, resulting in significant data transfer reduction. Our experiments demonstrate that the smart-KG+ significantly outperforms existing Web SPARQL interfaces on both pre-existing benchmarks for highly concurrent query execution as well as an accustomed query workload inspired by query logs of existing SPARQL endpoints.